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1. • CommentRowNumber1.
   • CommentAuthorbwebster
   • CommentTimeDec 2nd 2009
   • PermaLink
   Author: bwebster
   Format: MarkdownTaking the advice that if I write something on the internet, it should be stuck on the n-Lab, I've converted my recent comments in the n-category cafe and some old blog posts into a new page on the relationship between categorification and groupoidification: [[categorification via groupoid schemes]]

   Taking the advice that if I write something on the internet, it should be stuck on the n-Lab, I've converted my recent comments in the n-category cafe and some old blog posts into a new page on the relationship between categorification and groupoidification: categorification via groupoid schemes

2. • CommentRowNumber2.
   • CommentAuthorGuest
   • CommentTimeDec 2nd 2009
   • PermaLink
   Author: Guest
   Format: TextComments at [[categorification via groupoid schemes]] on terminology and notation for the first paragraph. David Roberts

   Comments at categorification via groupoid schemes on terminology and notation for the first paragraph.
   
   David Roberts
3. • CommentRowNumber3.
   • CommentAuthorbwebster
   • CommentTimeDec 2nd 2009
   • PermaLink
   Author: bwebster
   Format: MarkdownOk, I think I've addressed your questions, so I deleted the query box. Thanks, by the way; I'm sure the notation is still ghastly, but somehow the work "nerve" had slipped from my mind, and I didn't know about \rightrightarrows.

   Ok, I think I've addressed your questions, so I deleted the query box. Thanks, by the way; I'm sure the notation is still ghastly, but somehow the work "nerve" had slipped from my mind, and I didn't know about \rightrightarrows.

4. • CommentRowNumber4.
   • CommentAuthorbwebster
   • CommentTimeDec 2nd 2009
   • PermaLink
   Author: bwebster
   Format: MarkdownOh, the one part I was a bit unsure of is the question about a "groupoid of fintie sets" I meant a groupoid whose arrows and morphisms are finite, with no additional structure. Does "a groupoid of finite sets" mean something other than that?

   Oh, the one part I was a bit unsure of is the question about a "groupoid of fintie sets" I meant a groupoid whose arrows and morphisms are finite, with no additional structure. Does "a groupoid of finite sets" mean something other than that?

5. • CommentRowNumber5.
   • CommentAuthorGuest
   • CommentTimeDec 2nd 2009
   • PermaLink
   Author: Guest
   Format: TextI was thinking it could be interpreted as a groupoid whose objects are finite sets, say those arising as the F_q points of a scheme. David Roberts

   I was thinking it could be interpreted as a groupoid whose objects are finite sets, say those arising as the F_q points of a scheme.
   
   David Roberts
6. • CommentRowNumber6.
   • CommentAuthorGuest
   • CommentTimeDec 2nd 2009
   • PermaLink
   Author: Guest
   Format: TextI changed the first dotpoint to read 'finite groupoid', since that means the same thing as groupoid in FinSet David Roberts

   I changed the first dotpoint to read 'finite groupoid', since that means the same thing as groupoid in FinSet
   
   David Roberts
7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeDec 2nd 2009
   • PermaLink
   Author: Urs
   Format: MarkdownThanks for this entry! I edited it a bit (made the Theorem environment say "Theorem") and added some further links, for instance to [[motive]]. One question: you write "the motive of <latex> \mathbb{A}^1 </latex>" is pulling up through the projection <latex> X \times \mathbb{A}^1 \to X </latex> and then pushing down along it again. What is the terminology here: is this _operation_ itself called a motive? (All I know about motives comes from a very superficial encounter with Voevodsky's lecture notes.)

   Thanks for this entry!

   I edited it a bit (made the Theorem environment say "Theorem") and added some further links, for instance to motive.

   One question: you write "the motive of " is pulling up through the projection and then pushing down along it again.

   What is the terminology here: is this operation itself called a motive?

   (All I know about motives comes from a very superficial encounter with Voevodsky's lecture notes.)

8. • CommentRowNumber8.
   • CommentAuthorbwebster
   • CommentTimeDec 2nd 2009
   • PermaLink
   Author: bwebster
   Format: Markdownyeah, I decided it would probably be better to call that "multiplication by the motivic integral of $\mathbb{A}^1$."

   yeah, I decided it would probably be better to call that "multiplication by the motivic integral of $\mathbb{A}^1$."

9. • CommentRowNumber9.
   • CommentAuthorzskoda
   • CommentTimeApr 7th 2010
   • (edited Apr 7th 2010)
   • PermaLink
   Author: zskoda
   Format: MarkdownAs [[groupoidification]] appeared today again on the cafe, I have updated links, including the sbseminar links at [[Hecke algebra]]. I wish we had also a meaningful entry on [[Hall algebra]] but I am running out of time with so many things on the plate and other important deadlines approaching by this weekend. We should also understand the general connection between the motivic functions and groupoidification.

   As groupoidification appeared today again on the cafe, I have updated links, including the sbseminar links at Hecke algebra. I wish we had also a meaningful entry on Hall algebra but I am running out of time with so many things on the plate and other important deadlines approaching by this weekend.

   We should also understand the general connection between the motivic functions and groupoidification.

10. • CommentRowNumber10.
    • CommentAuthorbwebster
    • CommentTimeMay 2nd 2010
    • PermaLink
    Author: bwebster
    Format: MarkdownZoran, I'm not sure I understand what general connection you have in mind. I guess I tend to think of such a connection as factoring through the realization functor from motives to Galois representations, and thus going through well-understood mathematics.

    Zoran, I'm not sure I understand what general connection you have in mind. I guess I tend to think of such a connection as factoring through the realization functor from motives to Galois representations, and thus going through well-understood mathematics.